Symmetric Lamb Wave Research Articles

Internal Symmetrical Lamb Waves for High Phase Velocities

Internal Symmetrical Lamb Waves for High Phase Velocities

A variable kinematic multi-field model for lamb wave propagation analysis in smart composite panels

The study explores the propagation of symmetric and antisymmetric fundamental Lamb waves in laminated composite strips, employing multi-field piezo-elastic plate models. The findings indicate the necessity of employing higher-order kinematic models to enhance the accuracy of wave propagation assessments. To further optimize computational efficiency, node-dependent kinematic models are utilized. The research delves into the tradeoff between reducing computational costs and maintaining result accuracy demonstrating a reduction of up to 60% in computational expenses in simple models while keeping the error below 1%. Two-dimensional wave propagation in laminated composite plates was further considered, expanding the scope due to material orthotropy.

A guided wave propagation method for delamination detection in fiber-metal laminates

This study aimed to assess the delamination detection in FMLs via the finite element (FE) simulations of Lamb wave propagation. An FE model of an FML specimen with [Al/902/Al/902/Al] layup was developed. Delamination damage of 10 and 25 mm diameters was induced between different layers of the FML specimen. The fundamental antisymmetric Lamb wave mode (A0) at 60 kHz and the fundamental symmetric Lamb wave mode (S0) at the frequency of 206 kHz were propagated on the developed FE models. The Lamb wave phase velocity was obtained from the FE models and compared with those obtained from the Lamb wave propagation tests. The sensitivity of the A0 and S0 Lamb wave modes to the delamination and its diameter were examined. The inverse Lamb wave propagation problem was then solved, and the elastic modulus of the FML specimen was estimated in the intact and delamination regions. It was observed that the phase velocity of the S0 Lamb wave mode had a higher sensitivity to the delamination damage compared to that of the A0 Lamb wave mode. The phase velocity of the A0 Lamb wave mode was more sensitive to the delamination diameter. The capability of the proposed simulated Lamb wave propagation method as a virtual lab for detecting delamination in the FMLs was confirmed.

The Dispersion Calculator - a free software for calculating dispersion curves of guided waves

The nondestructive inspection of components by means of guided waves is an emerging technology in fields like aerospace or pipeline construction and maintenance. The guided waves' capability of propagating many meters in a structure is utilized for swift inspection tasks as well as structural health monitoring. The German Aerospace Center uses Lamb waves for the quality assurance of large-scale aerospace vehicle components made from carbon composites. However, the use of guided waves in NDT requires knowledge of the dispersion curves. DISPERSE is the most renown software for the calculation of dispersion curves. This paper presents the open source Dispersion Calculator (DC). The MATLAB® -based DC is an interactive and fully validated software for the computation of dispersion curves and mode shapes of guided waves in isotropic plates and multilayered anisotropic composites. Damping caused by viscoelasticity and fluid-loading can be considered. DC features the capability of calculating laminates consisting of several hundreds of layers so that even the largest specimens, like rocket booster pressure vessels, can be calculated. This is made possible through the implementation of the stiffness matrix method. DC is also able to distinguish the different mode families, like symmetric, antisymmetric, and nonsymmetric Lamb, shear horizontal, and Scholte waves, depending on the symmetry and coupling properties of a given layup. Lastly, DC features a highly efficient and robust dispersion curve tracing algorithm. DC is available at GitHub, and it has gained many users world-wide since its initial release in 2018.

A metasurface for suppressing mode conversion and achieving directional reflection of shear horizontal wave

The lowest-order shear horizontal (SH0) guided wave in a plate is crucial for nondestructive testing and structural health monitoring due to its nondispersive nature. However, mode conversion at the interface for the SH0 wave complicates the received information and increases the difficulty of signal analysis. In this work, an elastic metasurface is proposed to suppress mode conversion at the interface and to reflect the SH0 wave directionally. The metasurface comprises a series of rectangular elements with a specific phase gradient covering the 2π phase range. The effectiveness of the proposed metasurface is confirmed through finite element simulations and experimental validation. The results indicate that the metasurface can significantly reduce the amplitude of the reflected lowest-order symmetric Lamb wave when compared to the reflection without the metasurface, while simultaneously allowing the reflected SH0 wave to propagate at the designed angle. Furthermore, the metasurface maintains its functionality for SH0 wave with incident angles varying from 0° to 25°. This study provides a viable approach for suppressing mode conversion and modulating the reflection behavior of SH0 wave, which is expected to find applications in nondestructive testing and structural health monitoring.

Thermal stress estimation of a constrained metallic plate using symmetric and antisymmetric Lamb wave group velocities

This paper presents a technique for estimating thermal-induced stress in constrained metallic plates using the group velocity of Lamb waves, the accuracy of which is crucial for assessing the structural integrity and serviceability of metallic structures. However, without the ability to gauge the current stress levels, obtaining such measurements is technically challenging. To overcome this, we propose a thermal stress estimation technique that uses changes in the group velocities of the fundamental symmetric (S0) and antisymmetric (A0) Lamb wave modes caused by thermal and stress variations. First, this study introduces a theoretical-based zero-crossing algorithm to measure the group velocities of S0 and A0 Lamb wave modes. Next, leveraging the acoustoelastic coefficients corresponding to the S0 and A0 modes, which are determined before the plate’s installation, this study generates the lines depicting the changes in group velocity induced by temperature variations (CT) for both the S0 and A0 modes. These CT lines are derived from the lines illustrating changes in group velocity due to thermal stress variations (CTS), which are obtained after plate installation. Ultimately, the generated CT lines can be used to estimate thermal stress throughout the entirety of the plate’s operational life span by isolating the distinct stress variation effects from the CTS lines. The numerical validation results show favorable accuracy in thermal stress estimation in a constrained plate subjected to temperature variation using both S0 and A0 Lamb wave modes, with average errors of 0.63 % and 0.91 %, respectively.

Internal Symmetric Lamb Waves for High Phase Velocities

Internal Symmetric Lamb Waves for High Phase Velocities

Detecting Cracks on Plates Using Reflections of Fundamental Symmetric and Anti-symmetric Lamb Waves from Defect

Introduction: Ultrasonic Lamb waves can achieve long-range inspection on plate-like structures and can even detect unreachable cracks and defects. There are multiple modes under a certain generation frequency with most of them dispersive. Method: The dispersion curves of Lamb wave in a steel plate were given by numerical calculation. A 2-D finite element (FE) model of a steel plate was promoted. The fundamental symmetric and antisymmetric Lamb waves were generated by uploading symmetrical and anti-symmetrical displacements on one side of the plane. The wave reflects when it comes across the defect and the edge of the plate. Mode conversion will occur after the asymmetrical discontinuities of the structure. Result: The theoretical and numerical results of the values of group velocities of S0 and A0 in a steel plate show well agreement. The maximum amplitude of the converted A0 wave from the interaction of the incident S0 wave with the cracks was observed. The amplitude will first rise then fall under any depth of the defects. The relationship between the defect reflection and the length as well as the depth of defects were simulated based on the FE model. Phase reversion and phase delay were discovered by controlling the defect size changing in one dimension. The reflection coefficient increases linearly with the defect length while the depth is constant, as well as the defect depth while the length is constant. method: Using finite element (FE) method to simulate Lamb wave motion in a plate, as well as experiments on steel plates with artificial defects. Conclusion: Experiments on steel plates with artificial defects including thorough holes and tapered holes were carried out using ISONICA STAR. The results also show that when the defect size changes in one dimension such as the thorough holes, the reflection coefficient increases linearly correspondingly. However, the testing results of the taper holes were inconsistent with the regulation as the size increases in both the length and the depth. result: The values of group velocities were calculated by time-of-flight method to identify specific modes. The results were calibrated and showed well agreement with theoretical data. Mode conversion will appear when the wave comes across asymmetric discontinuities of the structure.

Robust transport and topological valley refraction of fundamental symmetric lamb waves in perforated phononic crystal plates

Lamb waves can be divided into antisymmetric Lamb waves (type A) and symmetric Lamb waves (type S), which are widely used in health monitoring of engineering structures and nondestructive evaluation of materials. However, due to the fact that each mode of Lamb wave has the setting group velocity in a certain bandwidth range, it is easy to cause the aliasing of multi-mode Lamb waves, partly limiting the application scenarios of Lamb wave. In this paper, a hexagonal lattice meta-structure is designed and the zero-order symmetric (S0) Lamb wave in a finite thickness plate is successfully separated. By breaking the spatial C 3v symmetry, a valley topological phononic crystal (PnC) plate for the pure S0 mode is constructed, and its robust topological transports are demonstrated. Firstly, the valley topological phase transition of S0 mode is realized by changing the angle of scatterer in PnC plate and the valley edge state of S0 mode is obtained. Furthermore, by introducing structural mismatch, it is verified that the edge state of S0 mode is robust to various bends and defect. Finally, by changing the material property of the terminal, the valley refraction with different directionality is realized. The results offer a route to individually study the symmetric modes of Lamb waves, and have potential application prospects in rapid and accurate ultrasonic nondestructive testing based on Lamb waves.

Determination of Young’s Modulus of PET Sheets from Lamb Wave Velocity Measurement

BackgroundThe elastic modulus of polyethylene terephthalate (PET) sheets is typically measured through destructive tests that require specific sample preparation and time-consuming testing procedures.ObjectiveTo improve the efficiency of measuring the elastic modulus of PET sheets, research on a non-destructive measurement approach using guided Lamb waves was conducted.MethodsIn this approach, the group velocity of the zero-order symmetric Lamb wave mode (S0 mode) at a single frequency is first measured from PET sheets. The semi-analytical finite element method (SAFEM) is used as the forward model to calculate the corresponding numerical group velocity. Particle swarm optimisation (PSO) is used to update the elastic modulus in the SAFEM model until the numerical group velocity from the model matches the experimental results.ResultsThe results show that measuring the group velocity data at a single frequency is sufficient for elastic modulus measurement while the material thickness can be assumed as a constant, which improves the efficiency of the measurement. The identified modulus differs from the tensile modulus of the material due to the frequency dependence of the elastic modulus. However, this discrepancy could be eliminated by using a linear regression model.ConclusionsThe method mentioned above can achieve non-destructive and efficient measurement of the elastic modulus of PET sheets, which can potentially be applied for in-line quality inspection in PET bottle production processes.

Mode-entangled resonance for lamb waves in a plate

We report a novel resonance phenomenon called the mode-entangled resonance. It can occur at a specific frequency in a plate carrying both symmetric and antisymmetric Lamb wave modes. We show that at this resonance, a symmetric or antisymmetric Lamb wave can be fully transmitted with its mode preserved from one plate to another through a matching plate geometrically misaligned with the two base plates. This phenomenon appears to be counter-intuitive because both symmetric and antisymmetric waves are generally formed in the reflected and transmitted wave fields when the misaligned plate is used as a matching plate. Our analysis shows that if both symmetric and antisymmetric Lamb wave modes at the resonance are entangled in the misaligned matching plate to satisfy the established phase matching condition, the matching plate fully transmits any wave mode across the two base plates. The discovered phenomenon is related to the classical Fabry-Perot resonance (FPR), but FPR is only applicable for single-mode transmission through a matching plate aligned with two base plates. Numerical and experimental results were presented to validate the discovered mode-entangled resonance phenomenon. Furthermore, we show that the discovered phenomenon can be used for super-amplification of the amplitude of the antisymmetric Lamb wave when it is excited by plate-surface-mounted patch transducers.

Classification of solutions for guided waves in fluid-loaded viscoelastic composites with large numbers of layers.

Guided ultrasonic waves are used for the inspection of multilayered composite aerospace structures. Calculating the corresponding dispersion diagrams is challenging for thick-walled composites with more than 100 layers, such as in modern rocket booster pressure vessels. The Dispersion Calculator (DC) is an open source software for calculating such dispersion diagrams and mode shapes of guided waves. Attenuation caused by viscoelasticity and fluid-loading makes the dispersion curve tracing much more difficult than in the nonattenuated case because the modal solutions are sought in the complex wavenumber plane. The tracing problem is mastered by a reliable algorithm. Whereas leaky Lamb and Scholte waves in coupled and decoupled cases are modeled using the stiffness matrix method, shear horizontal (SH) waves are traced using the transfer matrix method without facing the numerical instability. Through implementation of mode family specific dispersion equations in both matrix techniques for nonattenuated and attenuated cases, symmetric, antisymmetric, and nonsymmetric leaky Lamb, Scholte, and SH waves can be traced separately with better efficiency and robustness. The capabilities of DC are demonstrated by calculating dispersion diagrams and mode shapes for a viscoelastic composite with 400 layers immersed in water. Results are compared against DISPERSE (Imperial College London, London, UK) for selected cases.

Mode purification for multimode Lamb waves by shunted piezoelectric unimorph array

Guided wave-based nondestructive testing and structural health monitoring methods have been developed to exhibit attractive potentials and best prospects for rapid and sensitive detection of defects or damage in engineering structures. Different modes of guided waves can provide different sensitivities of damage detection. However, the multimode and mode conversion nature of guided waves poses significant challenges to mode purification of received signals. This study aims to design a metamaterial-based smart transducer for mode purification of Lamb waves in a plate, which can filter out an undesired mode of the Lamb wave to enhance sensing and actuating signals of a dominated mode. The smart transducer consists of a periodic array of shunted piezoelectric unimorphs with staggered polarization directions and is bonded on the surface of a host plate. Numerical and experimental results show that a local resonance bandgap for an anti-symmetric Lamb wave, rather than a symmetric Lamb wave, can be obtained and tuned through the shunting inductance circuit. Within such mode bandgap, the wave control for propagating a specific mode of the Lamb wave can be further realized, i.e., the mode of the Lamb wave is purified. The design presented herein offers enhanced capabilities in controlling guided wave propagation for engineering applications and nondestructive testing techniques.

An 8-inch commercial aluminum nitride MEMS platform for the co-existence of Lamb wave and film bulk acoustic wave resonators

This work investigates a co-design approach for fundamental symmetric Lamb wave (S0) resonators (LWR) and film bulk acoustic wave resonators (FBAR) in a commercial 8-inch aluminum nitride (AlN) microelectromechanical system (MEMS) platform to enable multi-band operation. The platform utilizes surface micromachining to define local release cavities, providing an undercut-free solution for acoustic resonators to achieve a high quality factor (Q). However, being based on a standardized platform initially tailored for FBAR devices, many design considerations and trade-offs need to be investigated for the co-existence between LWR and FBAR design. Hence, to capture the optimal design window for S0 LWRs while analyzing its performance impact on existing FBARs, the electrode configuration and its thickness are thoroughly investigated by the finite element method. In this work, a 2.2 GHz FBAR, a 700 MHz S0 LWR, and a 2.19 GHz S0 Lamé LWR are demonstrated for performance evaluation across different types of devices in this platform. The measurement results revealed a baseline performance for the FBAR device with an electromechanical coupling factor () of 6.73% and Q of 3017 at 2.2 GHz, resulting in a high figure-of-merit (FoM = ) over 200. In comparison, the 700 MHz S0 LWR exhibits a high Q of 2532 as well and a of 1.1% (FoM = 27.8), while the 2.19 GHz S0 Lamé LWR also exhibits a high Q of 1752 and a of 2.44% (FoM = 42.7), respectively. These performance indexes are all comparable with the current state-of-the-art, revealing the excellent potential of this AlN MEMS platform being implemented for future LWR development design or even mass production.

Topological Fano resonance of symmetric Lamb wave induced by antisymmetric trapped mode

The rapid development of topological physics in recent years has greatly enriched the methods for manipulating classic waves. Fano resonance is a widespread phenomenon featured with asymmetric and ultrasharp transmission line shape, which is induced by the constructive and destructive interference of two resonance modes with different quality factors. The temporal coupling mode theory is introduced to theoretically describe the physical process of Fano phenomena with two topological resonance states. The mechanism of the pass band led by the coupling between local resonance and Bragg scattering is introduced to design the antisymmetric topological resonance state and suppress the interference of the antisymmetric propagation mode. The complex eigenvalue analysis shows that the antisymmetric topological resonance state can be treated as the bound state in continuum (BIC). The periods of the phononic crystal (PnC) can be largely reduced by this scheme. The mechanism of coupling between two topological resonance modes attributed to geometric parameter variation is explained by the perturbing perspective and the temporal coupled mode theory. By theoretical analysis, the antisymmetric topological resonance state can be simultaneously treated as symmetric protected BIC and Friedrich–Wintgen BIC. Then, the design method for PnC with Fano resonance is proposed. The numerical results are in good agreement with the theoretical outcomes. The research results may find potential applications and offer the theoretical directive guideline for design in the fields of non-destructive testing, radio-frequency filters, resonators, and sensors.

A Lorentz Force EMAT Design with Racetrack Coil and Periodic Permanent Magnets for Selective Enhancement of Ultrasonic Lamb Wave Generation

This article proposes an electromagnetic acoustic transducer (EMAT) for selectively improving the purity and amplitude of ultrasonic Lamb waves in non-ferromagnetic plates. The developed EMAT consists of a racetrack coil and a group of periodic permanent magnets (PPMs). Two-dimensional finite element simulations and experiments are implemented to analyze the working mechanism and performance of the PPM EMAT. Thanks to the specific design, the eddy currents increase with increasing wire density and the directions of the magnetic fields and Lorentz forces alternate according to the polarities of the magnet units. Wires laid uniformly beneath the magnets, and the gaps between adjacent magnets generate tangential and normal Lorentz forces, resulting in-plane (IP) and out-of-plane (OP) displacements, respectively. The constructive interference occurs when the wavelength of the generated Lamb wave is twice the spacing of the magnets, leading to large amplitudes of the targeted ultrasonic Lamb waves. Therefore, the PPM EMAT is capable of generating pure symmetric or antisymmetric mode Lamb waves at respective frequencies. The results prove that the developed PPM EMAT can generate pure either S0 or A0 mode Lamb waves at respective frequencies. The increase in wire width and wire density further increases the signal amplitudes. Compared with the case of conventional meander-line-coil (MLC) EMAT, the amplitudes of the A0 and S0 mode Lamb waves of our PPM EMAT are increased to 880% and 328%, respectively.

Structural health monitoring of partially immersed metallic plates using nonlinear guided wave mixing

Metallic plates are important structural components of many liquid containment structures, such as liquid storage tanks and sewer pipes. Time-dependent loads can result in fatigue and degradation of the metallic material. Nonlinear guided wave mixing has been demonstrated to be sensitive to microstructural change at the early stage of material degradation. Previous studies have been carried out using the nonlinear guided wave mixing technique on various structures in gaseous environments. However, its application to structures immersed in liquid has not been explored. This paper numerically and experimentally investigates the nonlinear guided wave mixing in an aluminum plate loaded with water on one side. Experiments are carried out with an empty metal tank and the tank filled with water, respectively. The results show that cumulative generation of harmonics at the sum frequency due to the material nonlinearity of the partially immersed plate can be achieved by mixing the fundamental leaky symmetrical Lamb (leaky S0) waves at two different frequencies. Under the same experimental conditions, the amplitudes of the guided wave signals and the values of the relative nonlinearity parameters on the partially immersed plate are different from their counterparts on the plate without water. Finally, numerical simulations are performed with the material nonlinearity of the test plate simulated by the Murnaghan constitutive model. The numerical results reveal that both the second harmonics and the combination harmonics are sensitive to the material nonlinearity of the plate loaded with water on one side.

Construction of a mathematical model of lamb wave propagation in a steel pipeline with a protective outer coating

THE PURPOSE. Adapt the method of measuring the propagation of Lamb waves in thin two-layer plates to the study of the dependence of the phase velocity on the technical condition of pipelines with a protective outer coating. To perform a modification of the numerical-analytical algorithm for measuring the thickness of the coating and areas of non-adhesion of materials in thin two-layer plates for vibroacoustic diagnostics of technical pipelines. To investigate the propagation of a symmetric Lamb wave in a steel pipeline with a protective outer coating. METHODS. To solve the problem of localizing damage to technical pipelines, traditional methods of non-destructive testing based on vibroacoustic diagnostics are considered. RESULTS. Work on the construction of a mathematical model of the dependence of the propagation of the phase velocity of the Lamb wave on the thickness of the object under study has been carried out. The numerical analysis of the measurements was carried out using the example of thin two-layer segments of pipelines. The presence of changes in the thickness of the pipeline is taken as the effect of material defects on the propagation parameters of the Lamb wave mode. CONCLUSION. A numerical-analytical method for calculating the propagation of a symmetric Lamb wave mode in a thin segment is presented. The dependence of the propagation velocity of Lamb waves on the segment thickness is demonstrated. Based on the described technique, it seems possible to estimate not only the thickness of the segment and the area of non-adhesion of the layers, but also the total area of the defective area. This will allow in the future to record the relative changes in the thickness of the walls of pipelines to determine changes in the physical properties of the material or the presence of a defect.

Early damage detection of metallic plates with one side exposed to water using the second harmonic generation of ultrasonic guided waves

Metallic plates are the main structural components in a wide range of thin-walled structures under extreme operational conditions, such as nuclear cooling pipes, pressure vessels, rocket fuel tanks, and submarine hulls. These structures operate in extreme environments and are subjected to transient and repetitive loads. Real-time health monitoring of these structures is indispensable because they are vulnerable to fatigue and corrosion damage. Second harmonic generation is one of the reliable damage detection approaches to evaluate microstructural evolution and has been successfully applied to characterize initial damage on different structures in gaseous environments. However, there have been very limited studies on the second harmonics generation on the structures submerged in liquid. This paper experimentally and numerically investigates the feasibility of using second harmonic generation to evaluate the material degradation of metallic plates with one side exposed to water. The fundamental leaky symmetric Lamb wave mode (leaky S0) at low frequencies is selected because it has low-attenuation and weakly dispersive features, enabling approximate internal resonance. The experimental results show that the second harmonics of leaky S0 waves grow linearly with the propagation distance. The growth rate of the relative nonlinearity parameter (β′) can be related to the material nonlinearity of the one-side water-immersed plate. In addition, this study proposes a three-dimensional (3D) finite element (FE) model to simulate the generation of second harmonics in the one-side water-immersed plate. The material properties of the plate are modeled by the Murnaghan strain energy function. The Murnaghan constants of aluminum that describe the material nonlinearity at different fatigue levels are obtained from a previous experimental study. The simulation results demonstrate that the values of β′ change significantly with the material properties of the one-side water-immersed plates in the initial stages of fatigue damage. Thus, it can be concluded that the second harmonic generation techniques can be used for early damage detection of metallic plates with one side exposed to water.

Elastic Guided Waves in Bistable Composite Structures - Experimental and Numerical Investigation

Background: Bistable composite laminates are emerging as smart structures in automotive and aerospace applications. However, the behavior of the wave propagation within such laminates has not been investigated, which hinders their implementation in Structural Health Monitoring (SHM) and Non-Destructive Evaluation (NDE). Objective: As a result, this manuscript examines the propagation behavior of guided waves in bistable composite structures. By understanding the effect of pre-stressing in bistable composite laminates on the characteristics of propagating waves, such as velocity and amplitude, a more knowledgeable decision about their applications in flaw detection and assessment can be made. Methods: The fundamental symmetric (S0) and anti-symmetric (A0) Lamb wave modes were investigated during propagation in two bistable composite laminates, [0/90]T and [02/902]T, and were assessed experimentally and numerically using ABAQUS. For the tested frequencies, which ranged from 60 kHz to 250 kHz, the behavior of the propagating wave was evaluated for both stable configurations and across two different actuators that were lined up with the fiber directions. Signal processing techniques were thus extensively used to enhance the measured signals and identify both the group velocities and the amplitudes’ trend of the S0 and A0 wave modes. Results: Our results showed that there is a minimal variation (typically below 1%) in the amplitude and velocity of the A0 and S0 modes when the composite plates switch between the first stable configuration and the second stable configuration in both composite plates. These results were numerically validated by replicating the bi-stability of the composites. The numerical data were in relatively close agreement (10% average error) with the experimental values and trends. Furthermore, the bistable effect was examined in detail relative to a reference numerical flat (monostable) plate. Although the bistable effect induced a notable amount of internal residual stress, this did not significantly impact the propagating wave modes, with a maximum difference of about 2% when comparing wave velocities. Conclusions: The effect on the wave propagation behavior along different directions of both stable configurations was shown to be minimal. These results, which were validated numerically, clear the ambiguity on the usage of these laminates in experimental health monitoring.